Shuffler apparatus and related dynamic element matching technique for linearization of unit-element digital-to-analog converters

ABSTRACT

A data shuffler apparatus shuffles input bits to perform dynamic element matching. The shuffler apparatus includes N input shufflers, each input shuffler having N input terminals and N output terminals, each input terminal of each input shuffler receiving a respective one of the input bits. The apparatus also includes N output shufflers, each output shuffler having N input terminals and N output terminals, the input and output shufflers being interconnected such that each of the N output terminals of each input shuffler is connected to a respective input terminal of a different one of the N output shufflers.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Application No. 60/350,386, filed Jan. 24, 2002, entitled “Dynamic Element Matching Technique for Linearization of Unit-Element Digital-To-Analog Converters,” incorporated herein by reference in its entirety.

BACKGROUND OF THE INVENTION

In high resolution digital-to-analog converters (DACs), performance metrics such as linearity and noise are nominally determined by the matching of parameters derived from physical quantities in the construction of the DACs on an integrated circuit (IC), such as width, length, thickness, doping, etc. As a general rule, for each additional bit of performance in the DAC, parameter matching needs to be twice as tight. This translates to an increase by a factor of four in the IC area required by the DAC. When the DAC resolution is in the 16-bit range, it is no longer practical/economical to use size alone to achieve the required matching.

Over-sampled (sigma-delta) DACs (also referred to as “converters”) alleviate the need for raw matching using single-bit conversion (so called 1-bit DACs in CD players). A single-bit DAC has only two points in a transfer function of the DAC, and thus is inherently linear. The function of a sigma-delta modulator with a one-bit quantizer is to approximate a high resolution low frequency signal with a high frequency two-level signal. The drawback here is this produces large amounts of out-of-band, for example, high frequency, noise.

One solution is to use more than two levels of quantization. For example, 17 levels may be used. However, now linearity requirements are to the full resolution of the DAC. That is, for a 16-bit DAC, the transfer function of the DAC with these quantization levels must be collinear to 1 part in 2¹⁶, which is 1 part in 65,536. Such linearity is difficult to achieve with raw parameter matching of the single-bit DACs. Thus, there is need to achieve such linearity in a multi-level DAC using an alternative to raw parameter matching.

SUMMARY OF THE INVENTION

For high resolution over-sampled DACs, where the signal frequency band is much smaller than the sample rate of the DAC, there exists an opportunity to apply what is referred to as dynamic element matching to lessen the requirement for raw device matching. This is an entirely digital technique that operates on logic signals. Nominally, without dynamic element matching, mismatched single-bit DAC devices generate errors across all frequency bands, including low frequencies where the signals of interest reside. With dynamic element matching, these errors at the low frequencies (that is, in low frequency bands) are modulated to higher frequencies, outside the signal band of interest, where they can be substantially eliminated with a lowpass filter.

The present invention uses dynamic element matching of the single-bit DACs in a multi-bit DAC, to get full multi-bit (for example, 16-bit) accuracy. The main idea of dynamic element matching is to make each equally weighted unit element (that is, each single-element DAC) in the DAC perform equal work. For direct-current (DC) signals (that is, signals at zero Hz), the cancellation is perfect or nearly perfect. For low frequency signals, the errors are filtered with a 1st order highpass transfer function equal to (1−z⁻¹) in the frequency domain. In particular, the transfer function approximates sin(π f_(s)/2)/(π f_(s)/2), where f_(s) is the sample frequency.

The higher the over-sample ratio (where the over-sample ratio is defined as the sample frequency of the sigma-delta modulator over the signal frequency), the more effectively dynamic element matching can modulate the mismatch noise to out of band frequencies, that is, to frequencies away from the frequencies of interest.

According to an embodiment of the present invention, a data shuffler apparatus performs data shuffling of input bits to effect the dynamic element matching mentioned above. The data shuffler apparatus includes N input shufflers, each input shuffler having N input terminals and N output terminals, where N>2, each input terminal of each input shuffler receiving a respective one of the input bits. The shuffler apparatus also includes N output shufflers, each output shuffler having N input terminals and N output terminals, the input and output shufflers being interconnected such that each of the N output terminals of each input shuffler is connected to a respective input terminal of a different one of the N output shufflers (that is, each of the N output terminals of each input shuffler is connected to a respective input terminal of a different member of the set of N output shufflers). Each input and output shuffler is configured to output shuffled bits at its output terminals based on the input bits received at its input terminals, so as to balance (that is, equalize) the number of high-level logic bits outputted from each of the output terminals over time. In an embodiment, all of the shufflers operate in a substantially identical manner to each other.

Further embodiments of the present invention are described below.

BRIEF DESCRIPTION OF THE DRAWINGS/FIG.S

FIG. 1 is a block diagram of an example DAC apparatus in which the resent invention can be used.

FIG. 2 is a schematic/block diagram of an example 16×16 data shuffler apparatus (where N=4), including a plurality of 4×4 data shufflers, used in a thermometer decoder/shuffler module of FIG. 1.

FIG. 2A is an expanded view of the data shuffler apparatus of FIG. 2.

FIG. 3 is a block diagram of an example arrangement of a 4×4 data shuffler of FIG. 2.

FIG. 4 is a flow chart of an example method of shuffling data/logic bits sing an N×N data shuffler, such as the data shuffler of FIG. 3.

FIG. 4A is a flow chart of an example method of shuffling data/logic bits using a data shuffler apparatus, such as the data shuffler apparatus of FIG. 2A.

FIG. 5 is a list of assumptions used to perform a comparative simulation of the present invention.

FIG. 6 is a comparative plot of input amplitude (in dB) vs. Effective Number of Bits (ENOB) for different DACs, including a DAC using the 16×16 data shuffler apparatus of FIG. 2. The comparative plot was generated from the comparative simulation of FIG. 5.

FIG. 7 is an illustration as in FIG. 6, but using an expanded scale for input amplitude.

DETAILED DESCRIPTION OF THE INVENTION

As used herein, the terms “logic bits,” “logic signals,” and “bits” are used interchangeably to refer to the same signals. Also, the terms “high-level bit,” “logic ‘1’”, and “logic-one,” are interchangeable, as are the terms “low-level bit,” logic ‘0’”, and “logic-zero.”

FIG. 1 is a block diagram of an example DAC apparatus 100 in which the present invention can be used. DAC apparatus processes an input signal 102 having an exemplary sample rate of 2 Mega-samples/second (Ms/s). DAC apparatus 100 includes, in series, a halfband filter 105, an interpolator 110, a modulator 115, a thermometer decoder and shuffler module 120, a multi-bit thermometer DAC 125 including multiple single-bit DACs, a switched-capacitor filter 130, and a buffer 135. Exemplary signal and device characteristics, such as filter characteristics, signal sample rates, signal bit-widths, and signal voltages, are indicated at different stages of signal processing in FIG. 1.

In DAC apparatus 100, modulator 115 generates a 5-bit modulated signal 145, and provides the modulated signal to thermometer decoder and shuffler 120 (also referred to as module 120). Module 120 performs thermometer decoding, and logic-bit shuffling in accordance with the present invention. Thus, module 120 generates, from 5-bit modulated signal 145, a 16-bit shuffled thermometer-decoded signal 150, and provides signal 150 to thermometer DAC 125. Module 120 shuffles logic bits, in a manner to be described below, to achieve dynamic element (that is, single-bit DAC) matching in the present invention.

Thermometer DAC 125 includes multiple (for example, sixteen) single-bit DACs. Each single-bit DAC receives a respective bit of shuffled thermometer-decoded signal 150, and converts that bit to a corresponding analog voltage. DAC 125 combines the resulting sixteen converted voltages into a single analog signal 170.

FIG. 2 is a block diagram of an example arrangement of thermometer decoder and shuffler module 120. Module 120 includes a binary-to-thermometer decoder 205, followed by an example data shuffler apparatus 210 configured and operated in accordance with the principles of the present invention. Data shuffler apparatus 210 includes a plurality of substantially identical data sub-shufflers 215 (which are also referred to as shufflers 215, for convenience). In the example depicted in FIG. 2, data shuffler apparatus 210 includes eight shufflers 215.

Thermometer decoder 205 generates a thermometer decoded signal 220 from modulated signal 145, in a manner that is well known in the art. Thermometer decoded signal 220 includes bits 220 ₀-220 ₁₅ (arranged in a column in FIG. 2) representative of a 16-bit thermometer code. Thermometer decoder 205 provides decoded signal 220 to data shuffler apparatus 210. The plurality of shufflers 215, of data shuffler apparatus 210, are interconnected to each other and operate together in such a manner as to shuffle decoded bits 220 into shuffled, decoded bits 150.

FIG. 2A is an expanded view of data shuffler apparatus 210. Data shuffler apparatus 210 includes first stage or input shufflers IS₁-IS₄ (collectively, input shufflers 224), arranged in a first column of shufflers. Shuffler apparatus 210 also includes second stage or output shufflers OS₁-OS₄ (collectively, output shufflers 226), arranged in a second column of shufflers. An interconnection network 230 interconnects shufflers 224 and 226.

Each of shufflers IS₁-IS₄ and OS₁-OS₄ includes four input terminals IT₁-IT₄ and four output terminals OT₁-OT₄ (as indicated at input shuffler IS₁, for example). The input and output terminals are depicted as small square boxes coinciding with signal/connection lines in FIGS. 2 and 2A. As depicted in FIG. 2A, thermometer decoded bits 220 are divided into N (in this example, four) ordered sets of ordered bits 222 ₁-222 ₄. Each input shuffler IS₁, receives at its input thermals IT₁-IT₄ respective decoded bits of the ordered set of bits 222 _(i). For example, in the case where i=2, input shuffler IS₂ receives at its input terminals IT₁-IT₄ respective input bits 220 ₄-220 ₇ of ordered bit set 222 ₂.

Interconnection network 230 includes conductive traces/wires, or the like, that interconnect input shufflers IS₁-IS₄ with output shufflers OS₁-OS₄ according to the following generalized interconnection scheme or pattern: output terminal OT_(j) of input shuffler IS₁ is connected to input terminal IT₁ of output shuffler OS_(j), for i=1 . . . 4 and j=1 . . . 4.

For example, in the case where i=2 and j=3,

output terminal OT_(j=3) of input shuffler IS_(i=2) is connected to input terminal IT_(i=2) of output shuffler OS_(j=3).

Note that each input terminal IT_(i) (for example, input terminals IT₁ . . . IT₄) corresponds to an input bit position i (for example, ordered input bit positions 1-4, respectively). Similarly, each output terminal OT_(i) (for example, output terminals OT₁ . . . OT₄) corresponds to an output bit position i (for example, ordered output bit positions 1-4, respectively). Thus, input and output terminals can be thought of as being interchangeable with corresponding input and output bit positions in the present invention. The description herein uses subscripts to denote the different input and output terminals and corresponding bit positions.

In operation, each shuffler 215 shuffles the bits received at its input terminals, and outputs the shuffled received bits as output bits at its output terminals. For example, input shufflers IS₁-IS₄ separately shuffle respective input bit sets 222 ₁-222 ₄, and output respective bit sets, referred to as shuffled codes SC1 ₁-SC1 ₄. Each shuffled code SC_(i) includes shuffled bits, designated SB₁-SB₄ (as indicated, for example, at input shuffler IS₁), having ordered bit positions within that shuffled code in accordance with their respective subscript designations (1-4, for example).

Interconnection network 230 directs the bits of shuffled codes SC1 ₁-SC₄ into four different sets of bits, referred to as input codes IC₁-IC₄. In other words, interconnection network 230 forms input codes IC₁-IC₄ from shuffled codes SC1 ₁-SC1 ₄. Each input code IC includes bits, designated IB₁-IB₄ (as indicated, for example, at output shuffler OS₁), having ordered bit positions within that input code in accordance with their respective subscript designations. Specifically, interconnection network 230 causes input codes IC₁-IC₄ to be formed from the shuffled codes SC1 ₁-SC₄ in accordance with the following mapping pattern:

Bit SB_(j) of shuffled code SC1 ₁ is the same as bit IB_(i) of input code IC1 _(j), for i=1 . . . 4 and j=1 . . . 4.

For example, in the case where i=2 and j=3:

bit SB_(j=3) of shuffled code SC1 ₁₌₂ is the same as bit IB_(i=2) of input code OS_(j=3).

Output shufflers OS₁-OS₄ separately shuffle respective input codes IC₁-IC₄, and output respective shuffled bit sets, referred to as shuffled codes SC2 ₁-SC2 ₄.

In the example arrangement of shuffler apparatus 210 depicted in FIGS. 2 and 2A, each shuffler 215 includes four input terminals and four output terminals. Thus, each shuffler 215 is referred to as a 4×4 data shuffler. Similarly, shuffler apparatus 210 includes sixteen input terminals (the collective input terminals of input shufflers IS₁-IS₄) and sixteen output terminals (the collective output terminals of output shufflers OS₁-OS₄). Thus, shuffler apparatus 210 is referred to as a 16×16 data shuffler.

More generally, according to the present invention, an N²×N² shuffler apparatus includes 2N N×N shufflers, that is, N N×N input shufflers and N N×N output shufflers interconnected as described above, where N>1. For example, a 25×25 shuffler apparatus can be constructed using ten 5×5 shufflers. Such a shuffler includes five 5×5 input shufflers interconnected with five 5×5 output shufflers.

In the generalized shuffler apparatus arrangement having N input shufflers IS₁-IS_(N) and N output shufflers OS₁-OS_(N), where each shuffler has N input terminals and N output terminals, the connection pattern (and correspondingly, the mapping of coding bits) is generalized to: output terminal OT_(j) (bit SB_(j)) of input shuffler IS_(i) (code SC1 ₁) is connected to input terminal IT_(i) (bit IB₁) of output shuffler OS_(j) (code IC_(j)), for i=1. . . N and j=1. . . N.

FIG. 3 is a block diagram of an example arrangement of shuffler 215. Shuffler 215 includes input terminals IT₁-IT₄ (collectively, input terminals 302) and output terminals OT₁-OT₄ (collectively, output terminals 304). Shuffler 215 includes a bit generator 312 coupled between input and output terminals 302 and 304, a state controller 314 for controlling shuffler 215, and a score generator 316.

Shuffler 215 receives clock pulses, not shown, and operates on a cycle-by-cycle basis in response to the clock pulses. Over time, shuffler 215 receives successive sets of input bits at its input terminals 302, and generates a set of output bits at its output terminals 304 corresponding to each of the input bit sets. Shuffler 215 generates as set of output bits based on a corresponding set of input bits during a single cycle of the shuffler.

Over time, score generator 316 maintains a history of the number of high-level bits (that is, logic “1s”) that have been outputted from each of output terminals 304. For example, score generator 316 generates scores S₁-S₄ representative of an accumulated number of high-level bits (logic “1s”) that have been outputted from output terminals OT₁-OT₄, respectively. For example, score S₁ represents the number of “past” high-level bits that have been outputted from terminal OT₁, and so. Scores S₁-S₄ may be raw scores (that is, total accumulated high-level bits), or alternatively, relative scores, for example, scores that represent differences between the number of high-level bits that have been outputted from each of output terminals 304. Score generator 316 provides scores S₁-S₄ to state controller 314.

Input terminals IT₁-IT₄ receive respective input bits ib₁-ib₄ (collectively, input bits 320). In response to input bits 320 and scores S₁-S₄, state controller 314 maintains and updates an operational state of shuffler 215, as is described below. Based on the state of shuffler 215, state controller 314 generates a set of control signals 322 for controlling bit generator 312, and provides control signals 322 to the bit generator. In response to control signals 322 and input bits ib₁-ib₄, bit generator 312 produces output bits ob₁-ob₄ (collectively, output bits 324), and outputs these bits from output terminals OT₁-OT₄, respectively. In an arrangement of shuffler 215, bit generator 312 may include multiplexer logic to direct various ones of input bits 320 received at input terminals 302 (such as high-level bits) to various ones of output terminals 304, responsive to control signals 322. Specifically, bit generator 312:

(i) outputs from output terminals 304, a same number of high-level bits as are received at input terminals 302;

(ii) outputs the high-level bits from output terminals associated with lowest scores among output terminals 304; and

(iii) outputs the high-level bits from specific output terminals among output terminals 304 according to control signals 322, in a manner described below.

Further operational details of shuffler 215 are now described with reference to Tables 1 and 2, below. Table 1 includes a first (that is, left-most) column that lists all of the possible input bit combinations/sets for input bits 320. A second column lists the total number of high-level bits included in each bit combination in the first column.

TABLE 1 Input Bits: designations/positions ib₁ ib₂ ib₃ ib₄/ Total No. of 1 2 3 4 logic “1s” 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 2 0 1 0 0 1 0 1 0 1 2 0 1 1 0 2 0 1 1 1 3 1 0 0 0 1 1 0 0 1 2 1 0 1 0 2 1 0 1 1 3 1 1 0 0 2 1 1 0 1 3 1 1 1 0 3 1 1 1 1 4

Table 2 below is an example state transition table corresponding to shuffler 215, that is, the shuffler operates in accordance with the state transition table. Table 2, Column 1 (the left-most column) lists the possible total numbers of high-level bits that may be present at input terminals 320 at any given time. These totals are take from Column 2 of Table 1, above.

TABLE 2 Input Bits: Total No. of Output Bits: logic “1s” Current Next designations/positions (i.e., high- State State ob₁ ob₂ ob₃ ob₄/ level bits) (CS) (NS) 1 2 3 4 0 D D 0 0 0 0 A A 0 0 0 0 B B 0 0 0 0 C C 0 0 0 0 1 D A 1 0 0 0 A B 0 1 0 0 B C 0 0 1 0 C D 0 0 0 1 2 D B 1 1 0 0 A C 0 1 1 0 B D 0 0 1 1 C A 1 0 0 1 3 D C 1 1 1 0 A D 0 1 1 1 B A 1 0 1 1 C B 1 1 0 1 4 D D 1 1 1 1 A A 1 1 1 1 B B 1 1 1 1 C C 1 1 1 1

At any given time, shuffler 215 can be in any one of the following four possible operational states: state A, B, C or D. These states depend on the scores S₁-S₄ for the output terminals OT₁-OT₄ (that is, the scores for respective bit positions 1-4). The states are defined below:

State D: all of the scores S₁-S₄ are even. That is, the score for each output terminal (bit position) is equal to the score for each other output terminal (bit position);

State A: score S₁ for output terminal OT₁ (bit position 1) is ahead of the scores for all the other output terminals (bit positions) by a count of 1;

State B: scores S₁, S₂ for output terminals OT₁, OT₂ (bit positions 1, 2), are ahead of the other scores by a count of 1; and

State C: scores S₁, S₂, S₃ for output terminals OT₁, OT₂, OT₃ (bit positions 1, 2, 3) are ahead by 1.

Table 2, Column 2 lists, for each of the possible total number of high-level input bits listed in Column 1, the corresponding possible current states (CSs) that shuffler 215 may be in at any given time.

Table 2, Column 4 lists the output bit combinations (for example, combinations “0000,” “0101,” and so on) that shuffler 215 outputs from output terminals 304 in response to a given total of number of high-level input bits received by shuffler 215 (listed in Column 1) and a corresponding given current state of the shuffler (listed in Column 2).

Table 2, Column 3 lists the next state (NS) of shuffler 215 corresponding the current state and the total number of high-level input bits. In operation, for example, if the total number of high-level input bits applied to shuffler 215 is two (2), and the shuffler is in current state A (that is, score S₁ is ahead by one), then shuffler 215 outputs bit pattern “0110,” and transitions to next state C (that is, scores S₁, S₂, S₃ are ahead by one). If the total number of high-level input bits is two, and shuffler 215 is in current state C, then shuffler 215 outputs bit pattern “1001,” and transitions to next state A, and so on.

According to Table 2, shuffler 215 outputs high-level logic bits, if any, from output terminals/bit positions having successively numbered bit designations (for example, bit designations having increasing numbers), beginning with the output terminal/bit position having a lowest numbered bit designation among the output terminals/bit positions corresponding to the lowest scores. In cases where there are a sufficient number of high-level input bits, the high-level output bits roll-over from the highest or most significant bit position “4” to the lowest or least significant bit position “0.” In other words, the output bit positions produce high-level bits in a modulo-4 manner.

As mentioned above, over time, shuffler 215 equalizes the number of high-level bits output from (that is, produced at) output terminals OT₁-OT₄, and thus from bit positions 1-4. In one arrangement, shuffler 215 keeps score of the accumulated logic “1s” at each output terminal/bit position and directs logic “1s” received at the input terminals to the output terminals/bit position(s) having the lowest score(s). From the state transition table, it can be seen that the error in accumulated “1s” between any of the output terminals/bit positions corresponds to a difference of one, at most.

From the above, it is seen that each shuffler 215 in shuffler apparatus 210 is configured to:

(i) at any given time, generate the same number of logic-ones at its outputs as are present at its inputs; and

(ii) equalize over time the number of logic-ones generated at its respective outputs.

Thus, as a result of the operation of each of the shufflers 215 and the interconnections 230 between the shufflers 215 (that is between input and output shufflers 224 and 226), shuffler apparatus 210 is similarly configured to:

(i) at any given time, generate the same number of logic-ones at its outputs (that is, at the outputs corresponding to thermometer-decoded, shuffled signals 150 ₀-150 ₁₅) as are present at its inputs (that is, that are included in signals 220 ₀-220 ₁₅); and

(ii) equalize over time the number of logic-ones carried by each of the signals 150 ₀-150 ₁₅ (that is, at each of the bit positions corresponding to each of these logic signals).

Because each of the logic signals 150 ₀-150 ₁₅ (carrying equalized logic-ones) drives a respective one of the sixteen single-bit DACs in thermometer DAC 125, each of the single-bit DACs performs equal work over time. This results in dynamic element matching between the single-bit DACs because, over time, each of the single-bit DACs contributes essentially the same amount to summed output signal 170, and differences between single-bit DACs are averaged-out over time. For example, no one single-bit DAC dominates over time. Mathematically, over time, the number of accumulated “1s” for each output terminal/bit position is represented by the following expression(s):

N ₁₀=(N _(1i) +N _(2i) +N _(3i) +N _(4i))/4,

N ₂₀=(N _(1i) +N _(2i) +N ₃₁ +N _(4i))/4,

N ₃₀=(N _(1i) +N _(2i) +N _(3i) +N _(4i))/4,

N ₄₀=(N _(1i) +N _(2i) +N ₃₁ +N _(4i))/4, and

where each N_(io) (on the left-hand side of the equation) represents the number of accumulated “1s” for output terminal/bit position i, for i=1 . . . 4 (where each N_(io) corresponds to score S₁), and

each N_(ji) (on the right-side of the equation) represents the number of accumulated “1s” for input terminal/bit position j, for j=1 . . . 4 (on the right-side of the equation, “i” means “input”).

This implies the matching between the output bit positions is perfect for DC signals. For signals away from DC, the errors will be proportional to the highpass transfer function mentioned above.

In data shuffler apparatus 210, the following similar input/output relationship between accumulated “1s” follows from the signal flow caused by connection pattern 230:

Ot1=(In1+In2+ . . . +In16)/16

Out2=(In1+In2+ . . . +In16)/16

.

.

.

Out16=(In1+In2+ . . . +In16)/16

where: In1, In2, . . . , In16 represent the number of “1s” received at the respective inputs terminals of data shuffler apparatus 210 over time (for example, in respective signals 120 ₀, 120 ₁, . . . 120 ₁₅,), and

Out1, Out2, . . . Out16 represent the number of “1s” output from the output terminals of data shuffler apparatus 210 over time (for example, in respective signals 150 ₀, 150 ₁, . . . 150 ₁₆,).

In data shuffler apparatus 210, like shufflers 215, for DC signals, the outputs match perfectly or nearly perfectly. The use of shufflers 215 reduces the hardware complexity of 16×16 shuffler apparatus 210. Shuffler apparatus 210 of the present invention realizes dynamic element matching for 16-inputs to 16-outputs with substantially reduced hardware complexity compared to conventional dynamic element matching systems. For example, the entire state for a 16×16 shuffler can be implemented using only 16 flip-flops instead of 32 flip-flops in conventional systems, for example.

FIG. 4 is a flowchart of an example method 400 of shuffling input bits, that may be implemented in a shuffler, such as shuffler 215. The shuffler includes N input terminals and N output terminals, where N=4 for shuffler 215, for example.

A first step 405 includes determining over time for each output terminal (for example, output terminal OT₁) a respective score (for example, S_(i)) indicating an accumulated number of past, high-level logic bits that have been outputted from that output terminal.

A next step 410 includes receiving at the N input terminals respective logic bits. For example, in shuffler 215, this step includes receiving input bits ib₁-ib₄ at respective input terminals IT₁-IT₄.

A next step 415 includes outputting, from the N output terminals, a same number of high-level logic bits as are received at the N input terminals, where the same number is any number in the set 0 . . . N. This outputting step includes outputting the high-level logic bits, if any, from respective output terminals associated with lowest scores among the N output terminals. For example, in shuffler 215, bit generator 312 outputs, from output terminals 304, a same number of high-level logic bits as are received at input terminals 302. Bit generator 312 outputs the high-level logic bits, if any, from respective output terminals associated with lowest scores (S₁-S₄) among the output terminals.

Step 415 also includes outputting the high-level logic bits, if any, from output terminals having successively numbered bit designations, beginning with the output terminal having a lowest numbered bit designation among the output terminals having the lowest scores. This outputting arrangement can be seen in the state transition table (Table 2) described above.

A next step 420 includes updating the scores (for example, scores S₁-S₄) based on the logic bits outputted at step 415.

Steps 405-420 are repeated so as to equalize the accumulated scores (for example, scores S₁-S₄) over time.

FIG. 4A is a flowchart of an example method 450 of shuffling a plurality of input bits using a data shuffler apparatus, such as data shuffler apparatus 210. Method 450 achieves dynamic element matching of multiple DAC elements, such as the single-element DAC elements used in multi-element DAC 125.

A first step 455 includes dividing the plurality of input bits into N N-bit first input codes, where N>1. For example, this step includes forming input bit sets 222 ₁-222 ₄.

A next step 460 includes shuffling each input code (for example, codes 222 ₁-222 ₄) into a respective N-bit first shuffled code, thereby outputting N N-bit first shuffled codes having respective designations SC1 ₁ . . . SC1 _(N), the N bits of each first shuffled code having respective designations SB₁ . . . SB_(N) for that first shuffled code. The shuffling in this step may include the steps of method 400, for example. However, other data shuffling methods may be used.

A next step 465 includes forming, from the N first shuffled codes, N N-bit second input codes having respective designations IC₁ . . . IC_(N), the N bits of each second input code having respective designations IB₁ . . . IB_(N), wherein bit SB_(j) of first shuffled code SC1 _(i) is the same as bit IB₁ of input code IC_(j), where i=1 . . . N and j=1 . . . N.

A next step 470 includes shuffling each second input code into a respective N-bit second shuffled code. The data shuffling in this step may include the steps of method 400, for example. However, other data shuffling methods may be used.

FIG. 5 is a list of assumptions used to perform a comparative simulation of different DACs, including the DAC of the present invention using modulator 115 and shuffler apparatus 210.

FIG. 6 is a comparative plot of input amplitude (in dB) vs. Effective Number of Bits (ENOB) for different DACs, including the DAC of the present invention using modulator 115 and shuffler apparatus 210. The comparative plot was generated from the comparative simulation mentioned in connection with FIG. 5. The ENOB is a performance metric for the various DACs compared in the plots. The plot labeled “s16×16_(—)1” represents the performance of the DAC of the present invention. The plot labeled “ideal_candy” represents the performance of an ideal DAC having perfectly matched DAC elements (that is, a DAC having no mismatches).

FIG. 7 is an illustration as in FIG. 6, but using an expanded scale for input amplitude.

Conclusion

While various embodiments of the present invention have been described above, it should be understood that they have been presented by way of example, and not limitation. It will be apparent to persons skilled in the relevant art that various changes in form and detail can be made therein without departing from the spirit and scope of the invention.

The present invention has been described above with the aid of functional building blocks and method steps illustrating the performance of specified functions and relationships thereof. The boundaries of these functional building blocks and method steps have been arbitrarily defined herein for the convenience of the description. Alternate boundaries can be defined so long as the specified functions and relationships thereof are appropriately performed. Also, the order of method steps may be rearranged. Any such alternate boundaries are thus within the scope and spirit of the claimed invention. One skilled in the art will recognize that these functional building blocks can be implemented by discrete components, application specific intergrated circuits, processors executing appropriate software and the like or any combination thereof Thus, the breadth and scope of the present invention should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents. 

What is claimed is:
 1. A data shuffler apparatus for shuffling input bits, comprising: N input shufflers, each input shuffler having N input terminals and N output terminals, where N>2, each input terminal of each input shuffler receiving a respective one of the input bits; and N output shufflers, each output shuffler having N input terminals and N output terminals, the input and output shufflers being interconnected such that each of the N output terminals of each input shuffler is connected to a respective input terminal of a different one of the N output shufflers, each input and output shuffler being configured to output shuffled bits at its output terminals based on the input bits received at its input terminals.
 2. The apparatus of claim 1, wherein the input bits are divided into N ordered sets of input bits from a lowest ordered set of input bits to a highest ordered set of input bits, the N input terminals of each input shuffler receiving a corresponding one of the ordered sets of input bits.
 3. The apparatus of claim 2, wherein: the N input shufflers have respective input shuffler designations IS₁ . . . IS_(N) in accordance with the N ordered sets of input bits; the N input terminals of each output shuffler have respective input terminal designations IT₁ . . . IT_(N) for that shuffler; and each of the N output terminals of each input shuffler IS_(i), where i=1 . . . N, is connected to a respective input terminal IT_(i) of a respective one of the output shufflers, whereby each input shuffler IS_(i) is connected to each of the N output shufflers.
 4. The apparatus of claim 3, wherein: the N output shufflers have respective output shuffler designations OS₁ . . . OS_(N); the N output terminals of each input shuffler have respective output terminal designations OT₁ . . . OT_(N) for that shuffler; and each output terminal OT_(j), where j=1 . . . N, of each input shuffler IS_(i) is connected to the input terminal IT_(i) of the respective output shuffler OS_(j).
 5. The apparatus of claim 4, wherein each shuffler is configured to shuffle the N bits received at its N input terminals so as to (i) output from its N output terminals a same number of logic-one bits as are received at its N input terminals, and (ii) equalize over time the number of logic-one bits outputted from each of its N output terminals.
 6. The apparatus of claim 1, wherein N is greater than or equal to
 3. 7. The apparatus of claim 1, wherein the input bits are thermometer-decoded input bits, and each output terminal of each output shuffler represents a respective shuffler output terminal, the input and output shufflers being configured to shuffle the thermometer-encoded input bits so as to (i) output from the shuffler output terminals a same number of logic-one bits as are present in the thermometer encoded input bits, and (ii) equalize over time the number of logic-one bits outputted from the shuffler output terminals.
 8. A data shuffler apparatus, comprising: N input shufflers having respective designations IS₁ . . . IS_(N), where N>1, each input shuffler having N input terminals and N output terminals, the N output terminals having respective designations OT₁ . . . OT_(N), whereby the total number of input terminals is N² and the total number of output terminals is N², wherein N² input bits are received at the N² input terminals and N² output bits are output from the N² output terminals; and N output shufflers having respective designations OS₁ . . . OS_(N), each output shuffler having N input terminals and N output terminals, the N input terminals of each output shuffler having respective designations IT₁ . . . IT_(N) for that output shuffler, whereby the total number of input terminals is N² and the total number of output terminals is N², wherein N² input bits are received at the N² input terminals and N² output bits are output from the N² output terminals; the input and output shufflers being interconnected such that the output terminal OT_(j) of the input shuffler IS_(i) is connected to the input terminal IT_(i) of the output shuffler OS_(j), where i=1 . . . N and j=1 . . . N.
 9. The apparatus of claim 8, wherein the input shufflers and the output shufflers together shuffle the N² input bits received at the N² input shuffler input terminals into N² output bits output from the N² output terminals of the output shufflers.
 10. A method of shuffling a plurality of input bits, comprising: (a) dividing the input bits into N N-bit first input codes, where N>2; (b) shuffling each input code into a respective N-bit first shuffled code, thereby outputting N N-bit first shuffled codes having respective designations SC1 ₁ . . . SC1 _(N) the N bits of each first shuffled code having respective designations SB₁ . . . SB_(N) for that first shuffled code; (c) forming, from the N first shuffled codes, N N-bit second input codes having respective designations IC₁ . . . IC_(N), the N bits of each second input code having respective designations IB₁ . . . IB_(N), wherein bit SB_(j) of first shuffled code SC1 _(i) is the same as bit IB_(i) of input code IC_(j) where i=1 . . . N and j=1 . . . N; and (d) shuffling each second input code into a respective N-bit second shuffled code.
 11. The method of claim 10, wherein step (b) includes: outputting each first shuffled code such that it includes a same number of logic-one bits as are in the respective input code; and equalizing over time, in each first shuffled code, the number of logic-one bits outputted as bits SB₁ . . . SB_(N) in that first shuffled code.
 12. In a shuffler having N input terminals and N output terminals, where N>2, a method comprising: (a) determining over time, for each output terminal, a respective score indicating a number of past, logic-one bits that have been outputted from that output terminal; (b) receiving at the N input terminals respective logic bits; and (c) outputting, from the N output terminals, a same number of logic-one bits as are received at the input terminals, where the same number is any number in the set 0 . . . N, said outputting including outputting the logic-one bits, if any, from respective output terminals associated with lowest scores among the N output terminals.
 13. The method of claim 12, wherein step (c) includes outputting one or more logic-one bits from one or more respective output terminals having the lowest scores.
 14. The method of claim 12, further comprising, after step (c): (d) updating the scores based on the logic bits outputted at step (c); and (e) repeating steps (a) through (d), so as to equalize the scores over time.
 15. The method of claim 12, wherein the output terminals have respective numbered bit designations 1 . . . N, and step (c) comprises outputting the logic-one bits, if any, from output terminals having successively numbered bit designations, beginning with the output terminal having a lowest numbered bit designation among the output terminals having the lowest scores.
 16. The method of claim 12, further comprising, prior to step (c): maintaining a current operational state based on score combinations for the N outputs. 